MAX 3-SATConsider a propositional logical formula on NBoolean variables in conjunctive normal form (CNF), i.e., a conjunction (logical AND) of disjunctions (logical OR).Example:The truth assignment with and assigned to Trueand assigned to Falsesatisfies this formula. Each disjunction is also referred to as a “clause”.If each clause contains exactly k variables, the formula is a k-CNF formula.123233()()()xxxx∨¬∨∧∨∧¬1x2x3x

MAX 3-SAT cont.Problem: MAX-3-SATGiven a 3-CNF formula F, find a truth assignment that satisfies as many clauses as possible.The MAX 3-SAT problem is a so-called NP-hard problem; it is generally believed that no efficient (i.e., polynomial time) algorithm exists for solving such problems. [The $1M Clay Millennium prize, click on P=/=NP3]Note that we have a search space of 2Ntruth assignments.Stephen CookLeonid Levin

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